GRAND — Ground structure based topology optimization for arbitrary 2D domains using MATLAB

Zegard, Tomás; Paulino, Gláucio H.

doi:10.1007/s00158-014-1085-z

Cited by 117 publications

(56 citation statements)

References 19 publications

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“…The ground structure method has been refined, simplified and optimized, resulting in an easy-to-use implementation for truss topology optimization in structured orthogonal domains (Sokół 2011). Using an approach taken from computational geometry and the field of video-games, the method was extended to concave unstructured domains with the possibility of holes (Zegard and Paulino 2014a;2014b).…”

Section: Overview Of the Ground Structure Methodsmentioning

confidence: 99%

Bridging topology optimization and additive manufacturing

Zegard

Paulino

2015

Struct Multidisc Optim

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Topology optimization is a technique that allows for increasingly efficient designs with minimal a priori decisions. Because of the complexity and intricacy of the solutions obtained, topology optimization was often constrained to research and theoretical studies. Additive manufacturing, a rapidly evolving field, fills the gap between topology optimization and application. Additive manufacturing has minimal limitations on the shape and complexity of the design, and is currently evolving towards new materials, higher precision and larger build sizes. Two topology optimization methods are addressed: the ground structure method and density-based topology optimization. The results obtained from these topology optimization methods require some degree of post-processing before they can be manufactured. A simple procedure is described by which output suitable for additive manufacturing can be generated. In this process, some inherent issues of the optimization technique may be magnified resulting in an unfeasible or bad product. In addition, this work aims to address some of these issues and propose methodologies by which they may be alleviated. The proposed framework has applications in a number Electronic supplementary material The online version of this article (of fields, with specific examples given from the fields of health, architecture and engineering. In addition, the generated output allows for simple communication, editing, and combination of the results into more complex designs. For the specific case of three-dimensional density-based topology optimization, a tool suitable for result inspection and generation of additive manufacturing output is also provided.

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Section: Overview Of the Ground Structure Methodsmentioning

confidence: 99%

Bridging topology optimization and additive manufacturing

Zegard

Paulino

2015

Struct Multidisc Optim

Self Cite

381

210

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“…ensures that the combinatorial constraints are respected. This energy term also distinguishes our computational approach from the traditional ground structure method [Dorn 1964;Zegard and Paulino 2014], which often generates results with invalid connectivity con gurations, as illustrated in Figure 15. Optimization Algorithm.…”

Section: Continuous Optimizationmentioning

confidence: 99%

Design and volume optimization of space structures

et al. 2017

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Fig. 1. Le : A statically sound space structure designed and optimized with our framework, motivated by the real architectural project shown in Figure 2. Right: The space structure is constructed with six types of customized beams to minimize the total volume of the material used for beams while maintaining moderate manufacturing complexity. Here, a ho er color indicates a larger beam cross-section area. Our framework automatically determines the optimal cross-section areas of the six types of beams as well as the assignment of beam types.We study the design and optimization of statically sound and materially e cient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we rst jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with xed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and e ciency of the algorithms and the computational framework are validated by a variety of examples and comparisons.

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“…An optimum fibrous slab can be considered as analogue to an in-plane Michell structure, which is well known in the structural optimization research community; further development of the theory of Michell structures (Michell 1904) has been described by workers such as Chan (1967), Hemp (1973) and Lewinski et al (1994a, b). Also, a numerical means of identifying Michelltype structures using the "ground structure" approach was proposed by Dorn et al (1964) and further developed by workers such as Gilbert and Tyas (2003), Sokol (2014), and Zegard and Paulino (2014).…”

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confidence: 99%

Design of optimum grillages using layout optimization

Bołbotowski

Gilbert

2018

Struct Multidisc Optim

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Grillages are often used to form bridge decks and other constructions. However, following a period of intensive research activity in the 1970s, comparatively little attention has been paid to optimizing the layout of grillages in recent years. In this contribution a new numerical procedure is proposed which takes advantage of the adaptive solution scheme previously developed for truss layout optimization problems, enabling very large scale problems to be solved. A key benefit of the proposed numerical procedure is that it is completely general, and can therefore be applied to problems with arbitrary loading and boundary conditions. Also, unlike some previously proposed procedures, the sizes of individual beams can readily be discerned. To demonstrate its efficacy the numerical procedure is applied to a range of grillage layout design problems, including load dependent problems which could not be solved using traditional methods. It is shown that important phenomena such as "beam-weaves" can be faithfully captured and new high-precision numerical benchmark solutions are provided.

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GRAND — Ground structure based topology optimization for arbitrary 2D domains using MATLAB

Cited by 117 publications

References 19 publications

Bridging topology optimization and additive manufacturing

Bridging topology optimization and additive manufacturing

Design and volume optimization of space structures

Design of optimum grillages using layout optimization

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